1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differential Geometry: Showing a curve is a sphere curve

  1. Jan 24, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that a(x) =( -cos(2x)), -2*cos(x), sin (2x)) is a sphere curve by showing that (-1,0,0) belongs to each normal plane.

    2. Relevant equations
    Not quite sure (part of my question)
    T= a'(x)
    N= T'/norm(T')
    B= T x N (T cross N)
    3. The attempt at a solution

    Ok I found the values of the Tangent field, the Binormal Field, and the Normal field vectors to be certain values and have attempted to demonstrate, by finding a value of x for each of the fields, that the point exists for all three of the planes. However, I don't think this is what should have been done. In fact I am frankly confused as to how exactly to go about showing the asked statement is true. So I guess what I am asking for is did I do this right (see work below), or am I in the wrong frame of mind?

    T= (2 sin(2x), 2 sin(x), 2 cos(2x))
    N=( (4 cos(2x), 2 cos(x), -4sin(2x))/(sqrt(cos^2(x)+4)

    (B is kind of nasty to write up without latex...so I will work on that one, but for the time being if you need to figure it out just go with B = T cross N).

    Thanks for any help.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted